%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : TOP022+1 : TPTP v9.2.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:56:36 PM UTC 2026
% Result : Theorem 0.26s 1.62s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 7 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 59 ( 21 ~; 20 |; 12 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 64 ( 9 sgn 33 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m_8_2_2,conjecture,
! [X4,X5,X6] :
( ( path_connected(X4)
& a_member_of(X5,X4)
& a_member_of(X6,X4) )
=> isomorphic_groups(first_homotop_grp(X4,X5),first_homotop_grp(X4,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_8_2_2) ).
fof(m_8_2_1,axiom,
! [X1,X5,X6,X4] :
( a_path_from_to_in(X1,X5,X6,X4)
=> a_group_isomorphism_from_to(alpha_hat(X1),first_homotop_grp(X4,X5),first_homotop_grp(X4,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_8_2_1) ).
fof(path_connected_defn,axiom,
! [X4,X5,X6] :
( path_connected(X4)
<=> ( ( a_member_of(X5,X4)
& a_member_of(X6,X4) )
=> ? [X7] : a_path_from_to_in(X7,X5,X6,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_connected_defn) ).
fof(isomorphic_groups_defn,axiom,
! [X1,X2] :
( isomorphic_groups(X1,X2)
<=> ? [X3] : a_group_isomorphism_from_to(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isomorphic_groups_defn) ).
fof(i_0_4,negated_conjecture,
~ ! [X4,X5,X6] :
( ( path_connected(X4)
& a_member_of(X5,X4)
& a_member_of(X6,X4) )
=> isomorphic_groups(first_homotop_grp(X4,X5),first_homotop_grp(X4,X6)) ),
inference(assume_negation,[status(cth)],[m_8_2_2]) ).
fof(i_0_5,plain,
! [X38,X39,X40,X41] :
( ~ a_path_from_to_in(X38,X39,X40,X41)
| a_group_isomorphism_from_to(alpha_hat(X38),first_homotop_grp(X41,X39),first_homotop_grp(X41,X40)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_8_2_1])]) ).
fof(i_0_6,plain,
! [X28,X29,X30,X32,X33,X34,X35,X36,X37] :
( ( ~ path_connected(X28)
| ~ a_member_of(X29,X28)
| ~ a_member_of(X30,X28)
| a_path_from_to_in(esk2_3(X28,X29,X30),X29,X30,X28) )
& ( a_member_of(X33,X32)
| path_connected(X32) )
& ( a_member_of(X34,X32)
| path_connected(X32) )
& ( ~ a_path_from_to_in(X37,X35,X36,X32)
| path_connected(X32) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[path_connected_defn])])])])])]) ).
fof(i_0_7,plain,
! [X22,X23,X25,X26,X27] :
( ( ~ isomorphic_groups(X22,X23)
| a_group_isomorphism_from_to(esk1_2(X22,X23),X22,X23) )
& ( ~ a_group_isomorphism_from_to(X27,X25,X26)
| isomorphic_groups(X25,X26) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[isomorphic_groups_defn])])])])]) ).
fof(i_0_8,negated_conjecture,
( path_connected(esk3_0)
& a_member_of(esk4_0,esk3_0)
& a_member_of(esk5_0,esk3_0)
& ~ isomorphic_groups(first_homotop_grp(esk3_0,esk4_0),first_homotop_grp(esk3_0,esk5_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_4])])]) ).
cnf(i_0_9,plain,
( a_group_isomorphism_from_to(alpha_hat(X1),first_homotop_grp(X4,X2),first_homotop_grp(X4,X3))
| ~ a_path_from_to_in(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_5]),
[final] ).
cnf(i_0_10,plain,
( a_path_from_to_in(esk2_3(X1,X2,X3),X2,X3,X1)
| ~ path_connected(X1)
| ~ a_member_of(X2,X1)
| ~ a_member_of(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_6]),
[final] ).
cnf(i_0_11,plain,
( path_connected(X4)
| ~ a_path_from_to_in(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_6]),
[final] ).
cnf(i_0_12,plain,
( a_group_isomorphism_from_to(esk1_2(X1,X2),X1,X2)
| ~ isomorphic_groups(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7]),
[final] ).
cnf(i_0_13,plain,
( isomorphic_groups(X2,X3)
| ~ a_group_isomorphism_from_to(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_7]),
[final] ).
cnf(i_0_14,negated_conjecture,
~ isomorphic_groups(first_homotop_grp(esk3_0,esk4_0),first_homotop_grp(esk3_0,esk5_0)),
inference(split_conjunct,[status(thm)],[i_0_8]),
[final] ).
cnf(i_0_15,plain,
( a_member_of(X1,X2)
| path_connected(X2) ),
inference(split_conjunct,[status(thm)],[i_0_6]),
[final] ).
cnf(i_0_16,plain,
( a_member_of(X1,X2)
| path_connected(X2) ),
inference(split_conjunct,[status(thm)],[i_0_6]),
[final] ).
cnf(i_0_17,negated_conjecture,
a_member_of(esk5_0,esk3_0),
inference(split_conjunct,[status(thm)],[i_0_8]),
[final] ).
cnf(i_0_18,negated_conjecture,
a_member_of(esk4_0,esk3_0),
inference(split_conjunct,[status(thm)],[i_0_8]),
[final] ).
cnf(i_0_19,negated_conjecture,
path_connected(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_8]),
[final] ).
cnf(i_0_20,plain,
~ a_group_isomorphism_from_to(X1,first_homotop_grp(esk3_0,esk4_0),first_homotop_grp(esk3_0,esk5_0)),
inference(scs_inference,[],[i_0_14,i_0_13]) ).
cnf(i_0_21,plain,
( isomorphic_groups(X1,X2)
| ~ a_group_isomorphism_from_to(X3,X1,X2) ),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_22,plain,
~ a_path_from_to_in(X1,esk4_0,esk5_0,esk3_0),
inference(scs_inference,[],[i_0_14,i_0_13,i_0_9]) ).
cnf(i_0_23,plain,
( a_group_isomorphism_from_to(alpha_hat(X1),first_homotop_grp(X2,X3),first_homotop_grp(X2,X4))
| ~ a_path_from_to_in(X1,X3,X4,X2) ),
inference(rename_variables,[],[i_0_9]) ).
cnf(i_0_24,plain,
$false,
inference(scs_inference,[],[i_0_14,i_0_17,i_0_18,i_0_19,i_0_13,i_0_9,i_0_10]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : TOP022+1 : TPTP v9.2.1. Released v3.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n016.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 09:54:36 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 0.26/1.62 % Version : CSE_E---1.7
% 0.26/1.62 % Problem : theBenchmark.p
% 0.26/1.62 % SZS status Theorem for theBenchmark.p
% 0.26/1.62 % SZS output start CNFRefutation
% See solution above
% 0.26/1.65 % Total time : 1.273s
%------------------------------------------------------------------------------